Guided SAW device

ABSTRACT

A guided surface acoustic wave (SAW) device includes a substrate, a piezoelectric layer on the substrate, and a transducer on the piezoelectric layer. The substrate is silicon, and has a crystalline orientation defined by a first Euler angle (ϕ), a second Euler angle (θ), and a third Euler angle (ψ). The first Euler angle (ϕ), the second Euler angle (θ), and the third Euler angle (ψ) are chosen such that a velocity of wave propagation within the substrate is less than 5,400 m/s.

RELATED APPLICATIONS

This application claims the benefit of provisional patent applicationSer. No. 62/408,405, filed Oct. 14, 2016, the disclosure of which ishereby incorporated herein by reference in its entirety.

FIELD OF THE DISCLOSURE

The present disclosure relates to acoustic wave devices, and inparticular to guided acoustic wave devices configured to reduce one ormore spurious modes.

BACKGROUND

Acoustic wave devices are widely used in modern electronics. At a highlevel, acoustic wave devices include a piezoelectric material in contactwith one or more electrodes. Piezoelectric materials acquire a chargewhen compressed, twisted, or distorted, and similarly compress, twist,or distort when a charge is applied to them. Accordingly, when analternating electrical signal is applied to the one or more electrodesin contact with the piezoelectric material, a corresponding mechanicalsignal (i.e., an oscillation or vibration) is transduced therein. Basedon the characteristics of the one or more electrodes on thepiezoelectric material, the properties of the piezoelectric material,and other factors such as the shape of the acoustic wave device andother structures provided on the device, the mechanical signaltransduced in the piezoelectric material exhibits a frequency dependenceon the alternating electrical signal. Acoustic wave devices leveragethis frequency dependence to provide one or more functions.

Exemplary acoustic wave devices include surface acoustic wave (SAW)resonators and bulk acoustic wave (BAW) resonators, which areincreasingly used to form filters used in the transmission and receptionof RF signals for communication. Due to the stringent demands placed onfilters for modern RF communication systems, acoustic wave devices forthese applications must provide high quality factor, wide bandwidth(i.e., high electromechanical coupling coefficient), and favorabletemperature coefficient of frequency. Often, undesired oscillations orvibrations are transduced in the piezoelectric material of an acousticwave device, which degrade these characteristics. These undesiredoscillations or vibrations are often referred to as spurious modes.There is a need for acoustic wave devices with reduced spurious modessuch that the acoustic wave devices provide high quality factor, lowloss, favorable temperature coefficient of frequency, and highbandwidth.

SUMMARY

The present disclosure relates to acoustic wave devices, and inparticular to guided acoustic wave devices configured to reduce one ormore spurious modes. In one embodiment, a guided surface acoustic wave(SAW) device includes a substrate, a piezoelectric layer on thesubstrate, and a transducer on the piezoelectric layer. The substrate issilicon, and has a crystalline orientation defined by a first Eulerangle (ϕ), a second Euler angle (θ), and a third Euler angle (ψ). Thefirst Euler angle (ϕ), the second Euler angle (θ), and the third Eulerangle (ψ) are chosen such that a velocity of wave propagation within thesubstrate is less than 5,400 m/s. By limiting the velocity of wavepropagation in the substrate using the crystalline orientation of thesubstrate, higher order spurious modes may be suppressed, therebyimproving the performance of the guided SAW device.

In one embodiment, the first Euler angle (ϕ), the second Euler angle(θ), and the third Euler angle (ψ) are chosen such that a stopbandprovided by the guided SAW device has a bandwidth greater than 160 MHzand an integral quality of the guided SAW device is greater than 800,000within the stopband.

In one embodiment, the first Euler angle (ϕ), the second Euler angle(θ), and the third Euler angle (ψ) are chosen such that a peakconductance of lower frequency spurious modes below a series resonancefrequency of the guided SAW device is significantly reduced.

Those skilled in the art will appreciate the scope of the presentdisclosure and realize additional aspects thereof after reading thefollowing detailed description of the preferred embodiments inassociation with the accompanying drawing figures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

The accompanying drawing figures incorporated in and forming a part ofthis specification illustrate several aspects of the disclosure, andtogether with the description serve to explain the principles of thedisclosure.

FIG. 1 illustrates a guided surface acoustic wave (SAW) device accordingto one embodiment of the present disclosure.

FIG. 2 is a graph illustrating the admittance and its phase of a guidedSAW device according to one embodiment of the present disclosure.

FIGS. 3A-3D are graphs illustrating the admittance, conductance, andquality factor of a guided saw device according to one embodiment of thepresent disclosure.

FIGS. 4A-4D illustrate the cross-sectional view of a guided SAW deviceaccording to one embodiment of the present disclosure as well as theadmittance and conductance of the guided SAW device.

FIG. 5 is a graph illustrating a relationship between the velocity ofwave propagation in a substrate and a maximum thickness of apiezoelectric layer on the substrate to suppress higher order modesaccording to one embodiment of the present disclosure.

FIGS. 6A-6D illustrate the concept of Euler angles and how they describethe crystalline orientation of a material according to one embodiment ofthe present disclosure.

FIGS. 7A-7C illustrate the slowness curves and velocity variation withpropagation angle for different cuts of silicon.

FIGS. 8A-8C illustrate the admittance of a guided SAW device accordingto one embodiment of the present disclosure.

FIGS. 9A-9C illustrate a relationship between stopband width and thecrystalline orientation of a substrate of a guided SAW device accordingto one embodiment of the present disclosure.

FIGS. 10A-10C illustrate a relationship between peak conductance of oneor more spurious modes and the crystalline orientation of a substrate ofa guided SAW device according to one embodiment of the presentdisclosure.

FIGS. 11A-11C illustrate a relationship between stopband width, qualityfactor, lower frequency spurious mode suppression, higher order spuriousmodes suppression, and the crystalline orientation of a substrate of aguided SAW device according to one embodiment of the present disclosure.

FIG. 12 illustrates a guided SAW device according to one embodiment ofthe present disclosure.

DETAILED DESCRIPTION

The embodiments set forth below represent the necessary information toenable those skilled in the art to practice the embodiments andillustrate the best mode of practicing the embodiments. Upon reading thefollowing description in light of the accompanying drawing figures,those skilled in the art will understand the concepts of the disclosureand will recognize applications of these concepts not particularlyaddressed herein. It should be understood that these concepts andapplications fall within the scope of the disclosure and theaccompanying claims.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, these elements should notbe limited by these terms. These terms are only used to distinguish oneelement from another. For example, a first element could be termed asecond element, and, similarly, a second element could be termed a firstelement, without departing from the scope of the present disclosure. Asused herein, the term “and/or” includes any and all combinations of oneor more of the associated listed items.

It will be understood that when an element such as a layer, region, orsubstrate is referred to as being “on” or extending “onto” anotherelement, it can be directly on or extend directly onto the other elementor intervening elements may also be present. In contrast, when anelement is referred to as being “directly on” or extending “directlyonto” another element, there are no intervening elements present.Likewise, it will be understood that when an element such as a layer,region, or substrate is referred to as being “over” or extending “over”another element, it can be directly over or extend directly over theother element or intervening elements may also be present. In contrast,when an element is referred to as being “directly over” or extending“directly over” another element, there are no intervening elementspresent. It will also be understood that when an element is referred toas being “connected” or “coupled” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected” or “directly coupled” to another element, there are nointervening elements present.

Relative terms such as “below” or “above” or “upper” or “lower” or“horizontal” or “vertical” may be used herein to describe a relationshipof one element, layer, or region to another element, layer, or region asillustrated in the Figures. It will be understood that these terms andthose discussed above are intended to encompass different orientationsof the device in addition to the orientation depicted in the Figures.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the disclosure.As used herein, the singular forms “a,” “an,” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises,”“comprising,” “includes,” and/or “including” when used herein specifythe presence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this disclosure belongs. It willbe further understood that terms used herein should be interpreted ashaving a meaning that is consistent with their meaning in the context ofthis specification and the relevant art and will not be interpreted inan idealized or overly formal sense unless expressly so defined herein.

FIG. 1 shows details of a guided SAW device 10 according to oneembodiment of the present disclosure. The guided SAW device 10 includesa substrate 12, a piezoelectric layer 14 on the substrate 12, aninterdigital transducer 16 on a surface of the piezoelectric layer 14opposite the substrate 12, a first reflector structure 18A on thesurface of the piezoelectric layer 14 adjacent to the interdigitaltransducer 16, and a second reflector structure 18B on the surface ofthe piezoelectric layer 14 adjacent to the interdigital transducer 16opposite the first reflector structure 18A.

The interdigital transducer 16 includes a first comb electrode 20A and asecond comb electrode 20B, each of which include a number of electrodefingers 22 that are interleaved with one another as shown. A lateraldistance between adjacent electrode fingers 22 of the first combelectrode 20A and the second comb electrode 20B defines an electrodepitch P of the interdigital transducer 16. The electrode pitch P may atleast partially define a center frequency wavelength λ of the guided SAWdevice 10, where the center frequency is the primary frequency ofmechanical waves generated in the piezoelectric layer 14 by theinterdigital transducer 16. For a single electrode interdigitaltransducer 16 such as the one shown in FIG. 1, the center frequencywavelength λ is equal to twice the electrode pitch P. For a doubleelectrode interdigital transducer 16, the center frequency wavelength isequal to four times the electrode pitch P. A finger width W of theadjacent electrode fingers 22 over the electrode pitch P may define ametallization ratio M of the interdigital transducer 16, which maydictate certain operating characteristics of the guided SAW device 10.

In operation, an alternating electrical input signal provided at thefirst comb electrode 20A is transduced into a mechanical signal in thepiezoelectric layer 14, resulting in one or more acoustic waves therein.In the case of the guided SAW device 10, the resulting acoustic wavesare predominately surface acoustic waves. As discussed above, due to theelectrode pitch P and the metallization ratio M of the interdigitaltransducer 16, the characteristics of the material of the piezoelectriclayer 14, and other factors, the magnitude and frequency of the acousticwaves transduced in the piezoelectric layer 14 are dependent on thefrequency of the alternating electrical input signal. This frequencydependence is often described in terms of changes in the impedanceand/or a phase shift between the first comb electrode 20A and the secondcomb electrode 20B with respect to the frequency of the alternatingelectrical input signal. The alternating electrical potential betweenthe two comb electrodes 20A and 20B creates an electrical field in thepiezoelectric material which generate acoustic waves. The acoustic wavestravel at the surface and eventually are transducer back into anelectrical signal between the comb electrodes 20A and 20B. The firstreflector structure 18A and the second reflector structure 18B reflectthe acoustic waves in the piezoelectric layer 14 back towards theinterdigital transducer 16 to confine the acoustic waves in the areasurrounding the interdigital transducer 16.

In one embodiment, the substrate 12 is silicon and the piezoelectriclayer 14 is lithium tantalate. Specifically, the substrate 12 may besilicon cut at the (100) miller plane, the (110) miller plane, or the(111) miller plane. As discussed in detail below, the crystallineorientation of the substrate 12 may be translated from one of thesereference planes to increase the performance of the guided SAW device10. The piezoelectric layer may be 42° Y-X lithium tantalate. Thoseskilled in the art will appreciate that the principles of the presentdisclosure may apply to other materials for the substrate 12 and thepiezoelectric layer 14. The interdigital transducer 16, the firstreflector structure 18A, and the second reflector structure 18B maycomprise aluminum. While not shown to avoid obscuring the drawings,additional passivation layers, frequency trimming layers, or any otherlayers may be provided over all or a portion of the exposed surface ofthe piezoelectric layer 14, the interdigital transducer 16, the firstreflector structure 18A, and the second reflector structure 18B.Further, one or more layers may be provided between the substrate 12 andthe piezoelectric layer 14 in various embodiments.

FIG. 2 is a graph illustrating an ideal relationship of the admittance(shown by its amplitude and phase) between the first comb electrode 20Aand the second comb electrode 20B to the frequency of the alternatingelectrical input signal for the guided SAW device 10. A solid line 24illustrates the amplitude of the admittance between the first combelectrode 20A and the second comb electrode 20B with respect to thefrequency of the alternating electrical input signal. Notably, the solidline 24 includes a peak at a first point P1 at which the admittancebetween the first comb electrode 20A and the second comb electrode 20Bclimbs rapidly to a maximum value. This peak occurs at the seriesresonant frequency (f_(S)) of the guided SAW device 10. The impedancebetween the first comb electrode 20A and the second comb electrode 20Bis minimal at the series resonant frequency (f_(S)), such that the firstcomb electrode 20A and the second comb electrode 20B appear as ashort-circuit. The solid line 24 also includes a valley at a secondpoint P2 at which the admittance between the first comb electrode 20Aand the second comb electrode 20B plummets rapidly to a minimum value.This valley occurs at the parallel resonant frequency (f_(P)) of theguided SAW device 10. The impedance between the first comb electrode 20Aand the second comb electrode 20B is at a maximum at the parallelresonant frequency (f_(P)), such that an open circuit appears to bepresent between the first comb electrode 20A and the second combelectrode 20B.

A dashed line 26 illustrates the phase of the impedance between thefirst comb electrode 20A and the second comb electrode 20B with respectto the frequency of the alternating electrical input signal. Notably,the dashed line shows that a 180° phase shift occurs between the seriesresonant frequency (f_(S)) and the parallel resonant frequency (f_(P)).This phase shift is due to the change in the impedance from primarilycapacitive to primarily inductive between the series resonant frequency(f_(S)) and the parallel resonant frequency (f_(P)).

The graph shown in FIG. 2 is highly idealized. In reality, the responseof the guided SAW device 10 includes spurious areas that degrade theperformance thereof as discussed above. FIGS. 3A through 3D shownon-idealized responses of the guided SAW device 10. Specifically, FIG.3A is a graph illustrating the admittance of the guided SAW device 10,which is indicated by a solid line 28. As shown in FIG. 3A, the guidedSAW device 10 includes higher order spurious modes 30 above the parallelresonant frequency (f_(P)). FIG. 3B is a graph illustrating theconductance of the guided SAW device 10, which is indicated by a solidline 32. As shown in FIG. 3B, the guided SAW device 10 includes lowerfrequency spurious modes 34 below the series resonant frequency (f_(S)).FIG. 3C is a graph illustrating a stopband of the guided SAW device 10.A solid line 36 illustrates the absolute value of the admittance and adashed line 38 illustrates the real value of the admittance, whichindicates the stopband of the guided SAW device 10. A stopband widthW_(SB) is defined as the distance between rising edges of the real valueof the admittance illustrated by the dashed line 38. FIG. 3D is a graphillustrating the quality factor of the guided SAW device 10, which isindicated by a solid line 40. As discussed above, it is desirable tosuppress the higher order spurious modes and the lower frequencyspurious modes. Further, it is desirable to maximize the stopband widthW_(SB) and the quality factor.

As discovered by the inventors, one mechanism by which spurious modesare generated is the guidance of spurious waves within the piezoelectriclayer 14. Such wave guidance occurs when spurious waves are reflected bythe substrate 12 as illustrated in FIG. 4A, which is a cross-sectionalview of the guided SAW device 10 with arrows indicating the guidance ofspurious waves within the piezoelectric layer 14 due to reflectionthereof by the substrate 12. FIG. 4B is a graph illustrating the effectof this wave guide effect on the admittance of the guided SAW device 10,which is illustrated by a solid line 42. The conductance of the guidedSAW device 10 is illustrated with a dashed line 44. As illustrated,there are significant higher order spurious modes 46 above the parallelresonant frequency (f_(P)). Since the higher order spurious modes aredue to resonance inside the piezoelectric layer, their frequency andnumber depends mostly on the thickness of the piezoelectric layer 14. Ingeneral, when the piezoelectric thickness increases, the frequencyseparation between the modes is reduced and the number of spurious modesincreases. Generally, higher order spurious modes can be suppressed whenthey are above a cut-off frequency of the guided SAW device 10. Acut-off frequency 48 of the guided SAW device 10 is illustrated in FIG.4B by a sharp rise in the conductance thereof. The cut-off frequency 48of the guided SAW device 10 depends on a velocity of wave propagation inthe substrate 12, which is mostly dependent on the material propertiesof the substrate 12. When the frequency of the spurious waves is abovethe cut-off frequency 48 of the guided SAW device 10, the spurious wavesradiate into the substrate 12 and thus are suppressed, as illustrated inFIG. 4C. FIG. 4D is a graph illustrating the effect of this waveradiation effect on the admittance of the guided SAW device 10, which isillustrated by a solid line 50. The conductance of the guided SAW device10 is illustrated with a dashed line 52. As illustrated, there is asignificant reduction in higher order spurious modes.

As discussed above, the cutoff frequency depends mostly on the velocityin the substrate while the frequency of the spurious modes dependsmostly on the thickness of the piezoelectric layer 14. The spuriousmodes are suppressed when the cutoff frequency is between the resonancefrequency and the frequency of the first higher order spurious mode. Fora given substrate velocity, there exists a maximum piezoelectric layerthickness such that the spurious modes are all above the cutofffrequency or conversely, for a given piezoelectric layer thickness thereis a maximum substrate velocity such that the higher order modes aresuppressed.

As shown in FIG. 5, a maximum thickness of the piezoelectric layer 14 inorder to suppress higher order modes is proportional to a velocity ofwave propagation in the substrate. In FIG. 5, if the thickness of thepiezoelectric layer 14 is below the solid line, higher order modes canbe suppressed. As discussed above it is desirable to reduce the velocityof wave propagation in the substrate 12 in order to allow radiation ofspurious waves and thus reduction of higher order spurious modes withinthe wide range of thicknesses of the piezoelectric layer 14. Generally,it is desirable to limit the velocity of wave propagation in thesubstrate 12 to below 6000 m/s because the thickness of thepiezoelectric layer 14 can be more than 0.25λ when the velocity of wavepropagation in the substrate 12 is below 6000 m/s. If the thickness ofthe piezoelectric layer 14 is more than 0.25λ, the piezoelectric layer14 can be easily fabricated, since the thickness of the piezoelectriclayer 14 can be controlled at this level. As discussed above is thewavelength for the surface wave of the center frequency and is amultiple of the transducer period More preferably, it is desirable tolimit the velocity of wave propagation in the substrate 12 to below 5400m/s. In this case, the thickness of the piezoelectric layer 14 can bemore than 0.40λ, which makes fabrication of the piezoelectric layer 14even easier.

As further discussed above, the velocity of wave propagation in thesubstrate 12 is also dependent on the material properties of thesubstrate 12. In particular, the velocity of wave propagation in thesubstrate 12 is dependent on the crystalline orientation of thesubstrate 12. One way to describe the crystalline orientation of amaterial is using Euler angles. FIGS. 6A-6D illustrate the basicprinciples of how Euler angles describe a crystalline orientation of amaterial. FIG. 6A shows a coordinate system 54 including an x-axis 56, ay-axis 58, and a z-axis 60, all three of which are perpendicular to oneanother. A crystalline structure 62 is also illustrated. The crystallinestructure 62 is initially aligned with the coordinate system 54 suchthat the x-axis 56 is the direction of wave propagation therein and thez-axis 60 is the outward directed normal to the surface thereof. Aninitial cut plane 63 is perpendicular to the z-axis 60, with a wavepropagation direction indicated by an arrow provided therein.

FIG. 6B shows the coordinate system 54 and a first translated coordinatesystem 64, which is obtained by keeping the z-axis 60 stationary androtating the x-axis 56 toward the y-axis 58 to form a first translatedx-axis 66, a first translated y-axis 68, and a first translated z-axis70 (designated with a single prime indicator), which are allperpendicular to one another. A first Euler angle 72 is the angle formedbetween the x-axis 56 and the first translated x-axis 66. The firsttranslated z-axis 70 is coincident with the z-axis 60. The crystallinestructure 62 remains static while the cut plane 63 is translated intothe first translated coordinate system 64.

FIG. 6C shows the coordinate system 54 and a second translatedcoordinate system 74, which is obtained by keeping the first translatedx-axis 66 stationary and rotating the first translated z-axis 70 awayfrom the first translated y-axis 68 to form a second translated x-axis76, a second translated y-axis 78, and a second translated z-axis 80(designated with a double prime indicator), which are all perpendicularto one another. A second Euler angle 82, which is achieved afterobtaining the first Euler angle 72, is the angle formed between thez-axis 60 and the second translated z-axis 80. Since the firsttranslated z-axis 70 is coincident with the z-axis 60, the second Eulerangle 82 is equal to the angle formed between the first translatedz-axis 70 and the second translated z-axis 80. The first translatedx-axis 66 is coincident with the second translated x-axis 76. Again, thecrystalline structure 62 remains static while the cut plane 63 istranslated into the second translated coordinate system 74.

FIG. 6D shows the coordinate system 54 and a third translated coordinatesystem 84, which is obtained by keeping the second translated z-axis 80stationary and rotating the second translated x-axis 76 toward thesecond translated y-axis 78 to form a third translated x-axis 86, athird translated y-axis 88, and a third translated z-axis 90 (designatedwith a triple prime indicator), all of which are perpendicular to oneanother. A third Euler angle 92, which is achieved after obtaining thesecond Euler angle 82, is the angle formed between the second translatedx-axis 76 and the third translated x-axis 86. Since the first translatedx-axis 66 is coincident with the second translated x-axis 76, the thirdEuler angle 92 is equal to the angle formed between the first translatedx-axis 66 and the third translated x-axis 86. The second translatedz-axis 80 is coincident with the third translated z-axis 90. Again, thecrystalline structure 62 remains static while the cut plane 63 istranslated into the third translated coordinate system 84. The firstEuler angle 72 is referred to as Phi (ϕ), the second Euler angle 82 isreferred to as Theta (θ), and the third Euler angle 92 is referred to asPsi (ψ).

As will be appreciated by those skilled in the art, silicon crystal is acubic system of m3m, so its crystal structure is symmetric about the x,y, and z plane and the x, y, and z axes are interchangeable with eachother. Accordingly, the Euler angle to indicate a specific orientationof silicon is not unique. There are several sets of Euler angles toindicate the exact same orientation of Si. For example, Si(100) can beexpressed by Euler angles of (90°, 90°, ψ), (0°, 90°, ψ), (90°, 0°, ψ),(90°, 90°, ψ+90°), and so on, where (100) are Miller indices defining aplane along which the silicon is cut, as will be appreciated by thoseskilled in the art. In the description herein, certain definitions ofEuler angles to indicate Si(100), Si(110), and Si(111) may be used forpurposes of explanation and/or example, but those skilled in the artwill appreciate that all of the different definitions of Euler angles toindicate Si(100), Si(110), and Si(111) are contemplated herein.

To calculate the optimal crystalline orientation of the substrate 12,slowness curves for three base crystalline orientations for silicon weredetermined, as illustrated in FIGS. 7A through 7C. Each one of FIGS. 7Athrough 7C shows a slowness curve and a graph illustrating the velocityof wave propagation in the substrate 12 with respect to the propagationangle of the waves therein. FIG. 7A shows the results for silicon wherethe first and second Euler angles (ϕ,θ) are fixed according to the planedefined by Miller indices (100) e.g., (90°, 90°,ψ), FIG. 7B shows theresults for silicon where the first and second Euler angles (ϕ,θ) arefixed according to the plane defined by Miller indices (110) e.g.,(135°, 90°,ψ+35.264°), and FIG. 7C shows the results for silicon wherethe first and second Euler angles (ϕ,θ) are fixed according to the planedefined by Miller indices (111) e.g., (135°, 54.7356°, ψ). A slownesscurve is shown for each one of a longitudinal mode wave, a fast shearmode wave, and a slow shear mode wave, where the waves are propagatingin a direction defined by the third Euler angle (ψ). Each one of thegraphs similarly illustrates a velocity of each one of the longitudinalmode wave, the fast shear mode wave, and the slow shear mode wave withrespect to the third Euler angle (ψ). The cut-off frequency of theguided SAW device 10 is determined by the slowest wave type of thelongitudinal mode wave, the fast shear mode wave, and the slow shearmode wave.

To restrict the velocity of wave propagation in the substrate 12 below6,000 m/s, any of the reference cuts and any propagation angle ψ can beused. To restrict the velocity of wave propagation in the substrate 12below 5,400 m/s, only certain ranges of the third Euler angle (ψ) may beused in the case of the reference crystalline orientations show in FIGS.7A and 7B. In particular, when the first and second Euler angles (ϕ,θ)are fixed according to the miller plane (100) as in FIG. 7A, the thirdEuler angle (ψ) should be between 18° and 72° or between 108° and 162°to keep the velocity of wave propagation in the substrate 12 below 5400m/s. When the first and second Euler angles (ϕ,θ) are fixed according tothe miller plane (110) as in FIG. 7B, the third Euler angle (ψ) shouldbe between 0° and 34° or between 75° and 180° to keep the velocity ofwave propagation in the substrate 12 below 5400 m/s. When the first andsecond Euler angles (ϕ,θ) are fixed according to the miller plane (111)as in FIG. 7C, the third Euler angle (ψ) can be anywhere between 0° and180° to keep the velocity of wave propagation in the substrate 12 below5400 m/s.

Even when lowering the cut-off frequency by carefully selecting thecrystalline orientation of the substrate 12 as discussed above, there isa subset of crystalline orientations for the substrate 12 that providesuperior suppression of higher order spurious modes, as illustrated inFIGS. 8A through 8C. Each one of these figures shows the admittance ofthe guided SAW device 10 for different crystalline orientations of thesubstrate 12 with a fixed thickness (e.g., 0.4λ) of the piezoelectriclayer 14. Specifically, FIG. 8A shows the admittance for the guided SAWdevice 10 where the substrate 12 is defined by crystalline orientation(ϕ,θ,ψ)=(90°,90°,45°), FIG. 8B shows the admittance for the guided SAWdevice 10 where the substrate 12 is defined by the crystallineorientation (ϕ,θ,ψ)=(135°, 90°,35.264°), and FIG. 8C shows theadmittance for the guided SAW device 10 where the substrate 12 isdefined by the crystalline orientation (ϕ,θ,ψ)=(135°, 54.7356°,0°).While the crystalline orientation of the substrate 12 in each one ofFIGS. 8A through 8C ensures that the higher order spurious modes areabove a cut-off frequency illustrated by a vertical dashed line, thecrystalline orientation for the guided SAW device 10 in FIG. 8B providesthe largest reduction in higher order spurious modes, the crystallineorientation for the guided SAW device 10 in FIG. 8C provides the nextlargest reduction in higher order spurious modes, and the crystallineorientation for the guided SAW device 10 in FIG. 8A provides the lowestreduction in higher order spurious modes.

As discussed above, in addition to reducing higher order spurious modes,it is also desirable to maximize stopband width and quality factor. Todemonstrate this, FIGS. 9A through 9C each show two graphs, oneillustrating a relationship between stopband width and the crystallineorientation of the substrate 12 and the other illustrating arelationship between integral quality factor, which is defined by thetotal area under a quality factor curve within the stopband, and thecrystalline orientation of the substrate 12. Specifically, FIG. 9Aillustrates these relationships for the guided SAW device 10 includingthe substrate 12 where the first and second Euler angles (ϕ,θ) are fixedaccording to the miller plane (100) such that ϕ=90° and θ=90°, FIG. 9Billustrates these relationships for the guided SAW device 10 includingthe substrate 12 where the first and second Euler angles (ϕ,θ) are fixedaccording to the miller plane (110) such that ϕ=135° and θ=90° and thethird Euler angle ψ is offset by +35.264°, and FIG. 9C illustrates theserelationships for the guided SAW device 10 including the substrate 12where the first and second Euler angles (ϕ,θ) are fixed according to themiller plane (111) such that ϕ=135° and θ=54.7356°.

The graphs of the stopband width and the integral quality factor arealigned in order to see the overlap between maximized portions thereof.As illustrated, the crystalline orientation of the substrate 12 for theguided SAW device 10 in FIG. 9A provides the highest stopband width andintegral quality factor when the third Euler angle (ψ) is 0°±25° or90°±25°. Specifically, the stopband width of the guided SAW device 10 isat least 165 MHz and the integral quality factor is at least 880,000 atthese crystalline orientations. The crystalline orientation of thesubstrate 12 for the guided SAW device 10 in FIG. 9B provides thehighest stopband width and integral quality factor when the third Eulerangle (ψ) is 55°±25° or 145°±25°. Specifically, the stopband width ofthe guided SAW device 10 is at least 165 MHz and the integral qualityfactor is at least 900,000 at these crystalline orientations. Thecrystalline orientation of the substrate 12 for the guided SAW device 10in FIG. 9C provides the highest stopband width and integral qualityfactor when the third Euler angle (ψ) is 30°±15° or 90°±15° or 150°±15°.Specifically, the stopband width of the guided SAW device 10 is at least165 MHz and the integral quality factor is at least 920,000 at thesecrystalline orientations.

Further as discussed above, in addition to reducing higher orderspurious modes, maximizing stopband width, and maximizing qualityfactor, it is also desirable to reduce lower frequency spurious modes.To demonstrate this, FIGS. 10A through 10C each show two graphs, oneillustrating a relationship between peak conductance for a first lowfrequency spurious mode (see the larger peak of the lower frequencyspurious modes 34 shown in FIG. 3B, illustrated as a solid line) and asecond low frequency spurious mode (see the smaller peak of the lowerfrequency spurious modes 34 shown in FIG. 3B, illustrated as a dashedline) and the third Euler angle (ψ) of the substrate 12 and the otherillustrating a relationship between peak conductance of a combination ofthe first low frequency spurious mode and the second low frequencyspurious mode and the third Euler angle (ψ) of the substrate 12.Specifically, FIG. 10A illustrates these relationships for the guidedSAW device 10 including the substrate 12 where the first and secondEuler angles (ϕ,θ) are fixed according to the miller plane (100) suchthat ϕ=90° and θ=90°, FIG. 10B illustrates these relationships for theguided SAW device 10 including the substrate 12 where the first andsecond Euler angles (ϕ,θ) are fixed according to the miller plane (110)such that ϕ=135° and θ=90° and the third Euler angle ψ is offset by+35.264°, and FIG. 10C illustrates these relationships for the guidedSAW device 10 including the substrate 12 where the first and secondEuler angles (ϕ,θ) are fixed according to the miller plane (111) suchthat ϕ=135° and θ=54.7356°.

The graphs are aligned in order to see the overlap between minimizedportions of the low frequency spurious modes. As illustrated, thecrystalline orientation of the substrate 12 for the guided SAW device 10shown in FIG. 10A provides the highest suppression of lower frequencyspurious modes when the third Euler angle (ψ) is 0°±7.5°, 45°±7.5°,90°±7.5°, or 135°±7.5°. Specifically, the lower frequency spurious modeshave a peak conductance less than 0.01 Siemens at these crystallineorientations and for a simulated resonator used to obtain the valuesshown in the figure. The crystalline orientation of the substrate 12 forthe guided SAW device 10 shown in FIG. 10B provides the highestsuppression of lower frequency spurious modes when the third Euler angle(ψ) is 15°±7.5°, 55°±7.5°, 95°±7.5°, or 145°±7.5°. Specifically, thelower frequency spurious modes have a peak conductance less than 0.01Siemens at these crystalline orientations for the simulated resonator.The crystalline orientation of the substrate 12 for the guided SAWdevice 10 shown in FIG. 10C provides the highest suppression of lowerfrequency spurious modes when the third Euler angle (ψ) is 33°±10°,87°±10°, or 153°±10°. Specifically, the lower frequency spurious modeshave a peak conductance less than 0.1 Siemens at these crystallineorientations for the simulated resonator.

As shown above, certain crystalline orientations for the substrate 12reduce higher order spurious modes, maximize stopband width and qualityfactor, and reduce lower frequency spurious modes. Since it is desirableto simultaneously accomplish all of these tasks, it is advantageous todetermine the overlapping crystalline orientations that accomplish eachof these tasks. To demonstrate this, FIGS. 11A through 11C each showcharts illustrating optimal crystalline orientations for higher orderspurious mode suppression, wider stopband width and higher integralquality factor, and lower frequency spurious mode suppression.Specifically, FIG. 11A illustrates the optimal ranges for the thirdEuler angle (ψ) defining the crystalline orientation of the substrate 12where the first and second Euler angles (ϕ,θ) are fixed according to themiller plane (100) such that ϕ=90° and θ=90°, FIG. 11B illustrates theoptimal ranges for the third Euler angle (ψ) defining the crystallineorientation of the substrate 12 where the first and second Euler angles(ϕ,θ) are fixed according to the miller plane (110) such that ϕ=135° andθ=90° and the third Euler angle ψ is offset by +35.264°, and FIG. 11Cillustrates the optimal ranges for the third Euler angle (ψ) definingthe crystalline orientation of the substrate 12 where the first andsecond Euler angles (ϕ,θ) are fixed according to the miller plane (111)such that ϕ=135° and θ=54.7356°.

Specifically, a first shaded region 94 indicates the range of the thirdEuler angle (ψ) wherein a velocity of wave propagation in the substrate12 is less than 5,400 m/s as discussed above with respect to FIGS. 7Athrough 7C. A second shaded region 96 indicates the range of the thirdEuler angle (ψ) wherein a stopband provided by the guided SAW device 10has a bandwidth greater than 165 MHz and an integral quality factorwithin this stopband greater than 800,000 as discussed above withrespect to FIGS. 9A through 9C. A third shaded region 98 indicates therange of the third Euler angle (ψ) wherein a peak conductance of lowerfrequency spurious modes below the series resonance frequency (f_(S)) isless than 0.01 Siemens as discussed above with respect to FIGS. 10Athrough 10C. The overlapping regions of each illustrate the optimalregions for two or more of these parameters. The ideal range for thethird Euler angle (ψ) for each base crystalline orientation of silicondiscussed above is illustrated where all three of the first shadedregion 94, the second shaded region 96, and the third shaded region 98overlap.

As shown in FIG. 11A, there is no overlap for crystalline orientationsfor all of the above parameters. Accordingly, there is no range for thethird Euler angle (ψ) here that reduces both higher order and lowerfrequency spurious modes while maximizing stopband bandwidth andintegral quality factor. However, there is overlap between two or moreof the shaded regions and thus certain ranges for the third Euler angle(ψ) may provide multiple benefits. In FIG. 11B, there is overlap wherethe third Euler angle (ψ) is 145°±7.5°. This is illustrated by a fourthshaded region 100. Accordingly, these crystalline orientations for thesubstrate 12 will provide suppression of higher order spurious modes,wider stopband and higher quality factor, and suppression of lowerfrequency spurious modes. In FIG. 11C, there is overlap where the thirdEuler angle (ψ) is 33°±10°, 87°±10°, or 153°±10°. This is illustrated bythe fourth shaded region 100. Accordingly, these crystallineorientations for the substrate 12 will provide suppression of higherorder spurious modes, wider stopband and higher quality factor, andsuppression of lower frequency spurious modes.

As discussed above, the guided SAW device 10 may include layers betweenthe substrate 12 and the piezoelectric layer 14 in certain embodiments.For example, the guided SAW device 10 may include an oxide layer 102between the substrate 12 and the piezoelectric layer 14 as shown in FIG.12. The oxide layer 102 may be silicon dioxide or any other suitablematerial, and may have a thickness in the range of 0.08λ. In some cases,several layers can be inserted between the substrate 12 and thepiezoelectric layer 14. Impurities like fluorine can be implanted in thesilicon dioxide to reduce the temperature sensitivity of the device.

In some embodiments, the substrate 12 may be implanted or damaged withcertain elements to increase the resistivity thereof and decreasecarrier lifetime. For example, the substrate 12 may be implanted withsilicon, arsenic, krypton, beryllium, carbon, nitrogen, oxygen, neon, orany other suitable element. Further, the substrate 12 may be implantedwith deep “traps” so that electrical losses are reduced. These deep“traps” may be in the form of metal ions such as gold, vanadium, cobalt,zinc, copper, or any other suitable element. Further, these “traps” maybe provided in a separate layer. For example, a poly-silicon layer maybe provided between the substrate 12 and the oxide layer 102, or a layerof amorphous silicon may be provided between the substrate 12 and theoxide layer 102. Details of such embodiments can be found in co-assignedand co-pending U.S. Patent Publication No. 20170033764A1, the contentsof which are hereby incorporated by reference in their entirety.

While the principles of the present disclosure are discussed withrespect to a device including a single transducer, those skilled in theart will readily appreciate that the concepts discussed herein applyequally to devices including multiple transducers such as coupledresonator filters and the like.

Those skilled in the art will recognize improvements and modificationsto the preferred embodiments of the present disclosure. All suchimprovements and modifications are considered within the scope of theconcepts disclosed herein and the claims that follow.

What is claimed is:
 1. A guided surface acoustic wave (SAW) device comprising: a silicon substrate having a crystalline orientation defined by a first Euler angle (ϕ), a second Euler angle (θ), and a third Euler angle (ψ), wherein the first Euler angle (ϕ), the second Euler angle (θ), and the third Euler angle (ψ) are chosen such that a velocity of wave propagation within the substrate is less than 5,400 m/s; a piezoelectric layer on the silicon substrate; and a transducer on the piezoelectric layer.
 2. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (100); and the third Euler angle (ψ) is between one of 18°-72° and 108°-162°.
 3. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (110); and the third Euler angle (ψ) is between one of (0°-34°)+35.264° and (75°-180°)+35.264°.
 4. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (111); and the third Euler angle (ψ) is between 0°-180°.
 5. The guided SAW device of claim 1 wherein the piezoelectric layer comprises lithium tantalate.
 6. The guided SAW device of claim 5 wherein the transducer is an interdigital transducer comprising: a first comb electrode comprising a first bus bar and a first plurality of electrode fingers extending transversely from the first bus bar; and a second comb electrode comprising a second bus bar and a second plurality of electrode fingers extending transversely from the second bus bar such that: the first bus bar is parallel to the second bus bar; the first plurality of electrode fingers extend from the first bus bar towards the second bus bar; the second plurality of electrode fingers extend from the second bus bar towards the first bus bar; and the first plurality of electrode fingers are interleaved with the second plurality of electrode fingers.
 7. The guided SAW device of claim 1 wherein the transducer is an interdigital transducer comprising: a first comb electrode comprising a first bus bar and a first plurality of electrode fingers extending transversely from the first bus bar; and a second comb electrode comprising a second bus bar and a second plurality of electrode fingers extending transversely from the second bus bar such that: the first bus bar is parallel to the second bus bar; the first plurality of electrode fingers extend from the first bus bar towards the second bus bar; the second plurality of electrode fingers extend from the second bus bar towards the first bus bar; and the first plurality of electrode fingers are interleaved with the second plurality of electrode fingers.
 8. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (100); and the third Euler angle (ψ) is between one of 18°-25°, 65°-72°, 108°-115°, and 155°-162°.
 9. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (110); and the third Euler angle (ψ) is between one of (30°-34°)+35.264, (75°-80°)+35.264°, and (120°-170°)+35.264°.
 10. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (111); and the third Euler angle (ψ) is between 15°-45°, 75°-105°, and 135°-165°.
 11. The guided SAW device of claim 9 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (110); and the third Euler angle (ψ) is between (137.5°-152.5°)+35.264°.
 12. The guided SAW device of claim 10 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (111); and the third Euler angle (ψ) is between 23°-43°, 77°-97°, and 143°-163°.
 13. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (100); and the third Euler angle (ψ) is between one of 37.5°-52.5° and 127.5°-142.5°.
 14. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (110); and the third Euler angle (ψ) is between (7.5°-22.5°)+35.264°, (87.5°-102.5°)+35.264°, and (137.5°-152.5°)+35.264°.
 15. The guided SAW device of claim 1 wherein: the first Euler angle (ϕ) and the second Euler angle (θ) are fixed according to Miller plane (111); and the third Euler angle (ψ) is between 23°-43°, 77°-97°, and 143°-163°.
 16. The guided SAW device of claim 1 wherein a surface of the substrate on which the piezoelectric layer is provided is modified to reduce carrier lifetimes in the substrate.
 17. The guided SAW device of claim 16 wherein the surface of the substrate on which the piezoelectric layer is provided is subjected to ion implantation to reduce carrier lifetimes in the substrate.
 18. The guided SAW device of claim 16 wherein a polysilicon layer is provided between the substrate and the piezoelectric layer to reduce carrier lifetimes in the substrate.
 19. The guided SAW device of claim 16 wherein a layer of amorphous silicon is provided between the substrate and the piezoelectric layer to reduce carrier lifetimes in the substrate. 